Identifying the Influential Inputs for Network Output Variance Using Sparse Polynomial Chaos Expansion

Abstract

Sensitivity analysis (SA) is an important aspect of process automation. It often aims to identify the process inputs that influence the process output’s variance significantly. Existing SA approaches typically consider the input–output relationship as a black box and conduct extensive random sampling from the actual process or its high-fidelity simulation model to identify the influential inputs. In this article, an alternate, novel approach is proposed using a sparse polynomial chaos expansion-based model for a class of input–output relationships represented as directed acyclic networks. The model exploits the relationship structure by recursively relating a network node to its direct predecessors to trace the output variance back to the inputs. It, thereby, estimates the Sobol indices that measure the influence of each input on the output variance, accurately and efficiently. Theoretical analysis establishes the validity of the model as the prediction of the network output converges in probability to the true output under certain regularity conditions. Empirical evaluation of two manufacturing processes and a flooding process shows that the model estimates the Sobol indices accurately with far fewer observations than state-of-the-art black-box methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the problem of automated identification of the inputs that influence the variance of the output for networked processes without feedback control. Such processes arise in various natural and engineered systems, of which manufacturing operations and flood mitigation are of particular interest to us, where the output variance represents the uncertainty in productivity, quality, or cost. Therefore, influential inputs’ identification allows us to quantify the effects of the various process parameters, such as operating conditions and physical properties, in determining the uncertainties in the process outputs. We show that our identification method is guaranteed to quantify the effects accurately and is expected to do so more efficiently (with fewer experimental observations) than widely used stochastic sampling techniques. In the future, we will like to evaluate the usefulness of the developed method on large-scale manufacturing and supply chain networks in actual production facilities as well as on critical infrastructures subject to cascading failures.